\(\int \frac {e^{\frac {x^2+(2+x^2) \log ^2(x^2)+x \log (e^{4/5} x) \log ^2(x^2)}{x}} (x^2+(8+4 x^2) \log (x^2)+4 x \log (e^{4/5} x) \log (x^2)+(-2+x+x^2) \log ^2(x^2))}{x^2} \, dx\) [9649]

Optimal result

Integrand size = 86, antiderivative size = 26 \[ \int \frac {e^{\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}} \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx=e^{x+\left (\frac {2}{x}+x+\log \left (e^{4/5} x\right )\right ) \log ^2\left (x^2\right )} \]

[Out]

exp(x+ln(x^2)^2*(2/x+x+ln(x*exp(4/5))))

Rubi [F]

\[ \int \frac {e^{\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}} \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx=\int \frac {\exp \left (\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}\right ) \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx \]

[In]

Int[(E^((x^2 + (2 + x^2)*Log[x^2]^2 + x*Log[E^(4/5)*x]*Log[x^2]^2)/x)*(x^2 + (8 + 4*x^2)*Log[x^2] + 4*x*Log[E^
(4/5)*x]*Log[x^2] + (-2 + x + x^2)*Log[x^2]^2))/x^2,x]

[Out]

Defer[Int][E^(x + (4/5 + 2/x + x + Log[x])*Log[x^2]^2), x] + 4*Defer[Int][E^(x + (4/5 + 2/x + x + Log[x])*Log[
x^2]^2)*Log[x^2], x] + 8*Defer[Int][(E^(x + ((2 + x^2)*Log[x^2]^2)/x + Log[E^(4/5)*x]*Log[x^2]^2)*Log[x^2])/x^
2, x] + (16*Defer[Int][(E^(x + ((2 + x^2)*Log[x^2]^2)/x + Log[E^(4/5)*x]*Log[x^2]^2)*Log[x^2])/x, x])/5 + 4*De
fer[Int][(E^(x + ((2 + x^2)*Log[x^2]^2)/x + Log[E^(4/5)*x]*Log[x^2]^2)*Log[x]*Log[x^2])/x, x] + Defer[Int][E^(
x + (4/5 + 2/x + x + Log[x])*Log[x^2]^2)*Log[x^2]^2, x] - 2*Defer[Int][(E^(x + ((2 + x^2)*Log[x^2]^2)/x + Log[
E^(4/5)*x]*Log[x^2]^2)*Log[x^2]^2)/x^2, x] + Defer[Int][(E^(x + ((2 + x^2)*Log[x^2]^2)/x + Log[E^(4/5)*x]*Log[
x^2]^2)*Log[x^2]^2)/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx \\ & = \int \left (\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right )+\frac {4 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \left (10+4 x+5 x^2+5 x \log (x)\right ) \log \left (x^2\right )}{5 x^2}+\frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) (-1+x) (2+x) \log ^2\left (x^2\right )}{x^2}\right ) \, dx \\ & = \frac {4}{5} \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \left (10+4 x+5 x^2+5 x \log (x)\right ) \log \left (x^2\right )}{x^2} \, dx+\int \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \, dx+\int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) (-1+x) (2+x) \log ^2\left (x^2\right )}{x^2} \, dx \\ & = \frac {4}{5} \int \left (5 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )+\frac {10 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^2}+\frac {4 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x}+\frac {5 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log (x) \log \left (x^2\right )}{x}\right ) \, dx+\int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \, dx+\int \left (\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )-\frac {2 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x^2}+\frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x}\right ) \, dx \\ & = -\left (2 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x^2} \, dx\right )+\frac {16}{5} \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x} \, dx+4 \int \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right ) \, dx+4 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log (x) \log \left (x^2\right )}{x} \, dx+8 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^2} \, dx+\int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \, dx+\int \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right ) \, dx+\int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x} \, dx \\ & = -\left (2 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x^2} \, dx\right )+\frac {16}{5} \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x} \, dx+4 \int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \log \left (x^2\right ) \, dx+4 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log (x) \log \left (x^2\right )}{x} \, dx+8 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^2} \, dx+\int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \, dx+\int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \log ^2\left (x^2\right ) \, dx+\int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 5.12 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \frac {e^{\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}} \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx=e^{x+\left (\frac {4}{5}+\frac {2}{x}+x\right ) \log ^2\left (x^2\right )} x^{\log ^2\left (x^2\right )} \]

[In]

Integrate[(E^((x^2 + (2 + x^2)*Log[x^2]^2 + x*Log[E^(4/5)*x]*Log[x^2]^2)/x)*(x^2 + (8 + 4*x^2)*Log[x^2] + 4*x*
Log[E^(4/5)*x]*Log[x^2] + (-2 + x + x^2)*Log[x^2]^2))/x^2,x]

[Out]

E^(x + (4/5 + 2/x + x)*Log[x^2]^2)*x^Log[x^2]^2

Maple [A] (verified)

Time = 1.48 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35

method	result	size
parallelrisch	\({\mathrm e}^{\frac {x \ln \left (x^{2}\right )^{2} \ln \left (x \,{\mathrm e}^{\frac {4}{5}}\right )+\left (x^{2}+2\right ) \ln \left (x^{2}\right )^{2}+x^{2}}{x}}\)	\(35\)
risch	\(x^{\frac {8 i \pi \,\operatorname {csgn}\left (i x \right )}{x}} x^{-\frac {8 i \pi \,\operatorname {csgn}\left (i x^{2}\right )}{x}} x^{4 i x \pi \,\operatorname {csgn}\left (i x \right )} x^{-4 i x \pi \,\operatorname {csgn}\left (i x^{2}\right )} x^{-\frac {16 i \pi \,\operatorname {csgn}\left (i x^{2}\right )}{5}} x^{\frac {16 i \pi \,\operatorname {csgn}\left (i x \right )}{5}} x^{-\frac {\pi ^{2}}{2}} x^{2 \pi ^{2} \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )} x^{-\frac {3 \pi ^{2}}{2}} {\mathrm e}^{\frac {-5 x^{2} \pi ^{2} \operatorname {csgn}\left (i x^{2}\right )^{6}+20 x^{2} \pi ^{2} \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{5}-30 x^{2} \pi ^{2} \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )^{4}+20 x^{2} \pi ^{2} \operatorname {csgn}\left (i x \right )^{3} \operatorname {csgn}\left (i x^{2}\right )^{3}-5 x^{2} \pi ^{2} \operatorname {csgn}\left (i x \right )^{4} \operatorname {csgn}\left (i x^{2}\right )^{2}-4 x \,\pi ^{2} \operatorname {csgn}\left (i x^{2}\right )^{6}+16 x \,\pi ^{2} \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{5}-24 x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )^{4}+16 x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{3} \operatorname {csgn}\left (i x^{2}\right )^{3}-4 x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{4} \operatorname {csgn}\left (i x^{2}\right )^{2}+80 i x \ln \left (x \right )^{2} \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )-40 i x \ln \left (x \right )^{2} \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}-40 i x \ln \left (x \right )^{2} \pi \operatorname {csgn}\left (i x^{2}\right )^{3}-10 \pi ^{2} \operatorname {csgn}\left (i x^{2}\right )^{6}+40 \pi ^{2} \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{5}-60 \pi ^{2} \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )^{4}+40 \pi ^{2} \operatorname {csgn}\left (i x \right )^{3} \operatorname {csgn}\left (i x^{2}\right )^{3}-10 \pi ^{2} \operatorname {csgn}\left (i x \right )^{4} \operatorname {csgn}\left (i x^{2}\right )^{2}+80 x \ln \left (x \right )^{3}+80 x^{2} \ln \left (x \right )^{2}+64 x \ln \left (x \right )^{2}+160 \ln \left (x \right )^{2}+20 x^{2}}{20 x}}\)	\(537\)

[In]

int((4*x*ln(x^2)*ln(x*exp(4/5))+(x^2+x-2)*ln(x^2)^2+(4*x^2+8)*ln(x^2)+x^2)*exp((x*ln(x^2)^2*ln(x*exp(4/5))+(x^
2+2)*ln(x^2)^2+x^2)/x)/x^2,x,method=_RETURNVERBOSE)

[Out]

exp((x*ln(x^2)^2*ln(x*exp(4/5))+(x^2+2)*ln(x^2)^2+x^2)/x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.50 \[ \int \frac {e^{\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}} \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx=e^{\left (\frac {5 \, x \log \left (x^{2}\right )^{3} + 2 \, {\left (5 \, x^{2} + 4 \, x + 10\right )} \log \left (x^{2}\right )^{2} + 10 \, x^{2}}{10 \, x}\right )} \]

[In]

integrate((4*x*log(x^2)*log(x*exp(4/5))+(x^2+x-2)*log(x^2)^2+(4*x^2+8)*log(x^2)+x^2)*exp((x*log(x^2)^2*log(x*e
xp(4/5))+(x^2+2)*log(x^2)^2+x^2)/x)/x^2,x, algorithm="fricas")

[Out]

e^(1/10*(5*x*log(x^2)^3 + 2*(5*x^2 + 4*x + 10)*log(x^2)^2 + 10*x^2)/x)

Sympy [A] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.38 \[ \int \frac {e^{\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}} \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx=e^{\frac {x^{2} + x \left (\frac {\log {\left (x^{2} \right )}}{2} + \frac {4}{5}\right ) \log {\left (x^{2} \right )}^{2} + \left (x^{2} + 2\right ) \log {\left (x^{2} \right )}^{2}}{x}} \]

[In]

integrate((4*x*ln(x**2)*ln(x*exp(4/5))+(x**2+x-2)*ln(x**2)**2+(4*x**2+8)*ln(x**2)+x**2)*exp((x*ln(x**2)**2*ln(
x*exp(4/5))+(x**2+2)*ln(x**2)**2+x**2)/x)/x**2,x)

[Out]

exp((x**2 + x*(log(x**2)/2 + 4/5)*log(x**2)**2 + (x**2 + 2)*log(x**2)**2)/x)

Maxima [A] (verification not implemented)

none

Time = 0.40 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.19 \[ \int \frac {e^{\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}} \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx=e^{\left (4 \, x \log \left (x\right )^{2} + 4 \, \log \left (x\right )^{3} + \frac {16}{5} \, \log \left (x\right )^{2} + x + \frac {8 \, \log \left (x\right )^{2}}{x}\right )} \]

[In]

integrate((4*x*log(x^2)*log(x*exp(4/5))+(x^2+x-2)*log(x^2)^2+(4*x^2+8)*log(x^2)+x^2)*exp((x*log(x^2)^2*log(x*e
xp(4/5))+(x^2+2)*log(x^2)^2+x^2)/x)/x^2,x, algorithm="maxima")

[Out]

e^(4*x*log(x)^2 + 4*log(x)^3 + 16/5*log(x)^2 + x + 8*log(x)^2/x)

Giac [F]

\[ \int \frac {e^{\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}} \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx=\int { \frac {{\left ({\left (x^{2} + x - 2\right )} \log \left (x^{2}\right )^{2} + 4 \, x \log \left (x^{2}\right ) \log \left (x e^{\frac {4}{5}}\right ) + x^{2} + 4 \, {\left (x^{2} + 2\right )} \log \left (x^{2}\right )\right )} e^{\left (\frac {x \log \left (x^{2}\right )^{2} \log \left (x e^{\frac {4}{5}}\right ) + {\left (x^{2} + 2\right )} \log \left (x^{2}\right )^{2} + x^{2}}{x}\right )}}{x^{2}} \,d x } \]

[In]

integrate((4*x*log(x^2)*log(x*exp(4/5))+(x^2+x-2)*log(x^2)^2+(4*x^2+8)*log(x^2)+x^2)*exp((x*log(x^2)^2*log(x*e
xp(4/5))+(x^2+2)*log(x^2)^2+x^2)/x)/x^2,x, algorithm="giac")

[Out]

integrate(((x^2 + x - 2)*log(x^2)^2 + 4*x*log(x^2)*log(x*e^(4/5)) + x^2 + 4*(x^2 + 2)*log(x^2))*e^((x*log(x^2)
^2*log(x*e^(4/5)) + (x^2 + 2)*log(x^2)^2 + x^2)/x)/x^2, x)

Mupad [B] (verification not implemented)

Time = 13.76 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.58 \[ \int \frac {e^{\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}} \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx=x^{{\ln \left (x^2\right )}^2}\,{\mathrm {e}}^{\frac {2\,{\ln \left (x^2\right )}^2}{x}}\,{\mathrm {e}}^{\frac {4\,{\ln \left (x^2\right )}^2}{5}}\,{\mathrm {e}}^x\,{\mathrm {e}}^{x\,{\ln \left (x^2\right )}^2} \]

[In]

int((exp((log(x^2)^2*(x^2 + 2) + x^2 + x*log(x^2)^2*log(x*exp(4/5)))/x)*(log(x^2)*(4*x^2 + 8) + log(x^2)^2*(x
+ x^2 - 2) + x^2 + 4*x*log(x^2)*log(x*exp(4/5))))/x^2,x)

[Out]

x^(log(x^2)^2)*exp((2*log(x^2)^2)/x)*exp((4*log(x^2)^2)/5)*exp(x)*exp(x*log(x^2)^2)